• Korean Journal of Microbiology
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• v.54 no.4
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• pp.420-427
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• 2018

The orthogonal pair of Saccharomyces cerevisiae tyrosyl-tRNA synthetase (Sc YRS) and a variant of E. coli initiator tRNA, fMam $tRNA_{CUA}$ which recognizes the amber stop codon is an effective tool for site-specific incorporation of unnatural amino acids into the protein in E. coli. To evolve the amber suppression activity of the orthogonal pair, we generated a mutant library of Sc YRS by randomizing two amino acids at 320 and 321 which involve recognition of the first base of anticodon in fMam $tRNA_{CUA}$. Two positive clones are selected from the library screening with chloramphenicol resistance mediated by amber suppression. They showed growth resistance against high concentration of chloramphenicol and their $IC_{50}$ values were approximately 1.7~2.3 fold higher than the wild type YRS. In vivo amber suppression assay reveals that mutant YRS-3 (mYRS-3) clone containing amino acid substitutions of P320A and D321A showed 6.5-fold higher activity of amber suppression compared with the wild type. In addition, in vitro aminoacylation kinetics of mYRS-3 also showed approximately 7-fold higher activity than the wild type, and the enhancement was mainly due to the increase of tRNA binding affinity. These results demonstrate that optimization of anticodon recognition by engineered aminoacyl tRNA synthetase improves the efficiency of unnatural amino acid incorporation in response to nonsense codon.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.565-575
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• 2013

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.185-202
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• 2019

In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form $$\{u^{\Delta}(t)=Au(t)+f(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ and $$\{u^{\Delta}(t)=Au(t)+f(t,u),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ in terms of the stability of the homogeneous equation $$\{u^{\Delta}(t)=Au(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ where f is rd-continuous in $t{\in}{\mathbb{T}}$ and with values in a Banach space X, with f(t, 0) = 0, and A is the generator of a $C_0$-semigroup $\{T(t):t{\in}{\mathbb{T}}\}{\subset}L(X)$, the space of all bounded linear operators from X into itself. Here D(A) is the domain of A and ${\mathbb{T}}{\subseteq}{\mathbb{R}}^{{\geq}0}$ is a time scale which is an additive semigroup with property that $a-b{\in}{\mathbb{T}}$ for any $a,b{\in}{\mathbb{T}}$ such that a > b. Finally, we give illustrative examples.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.483-494
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• 2017

In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power nonlinearity given in the following form: $$T_{\lambda}(f;x)={\int_a^b}{\sum^n_{m=1}}f^m(t)K_{{\lambda},m}(x,t)dt,\;{\lambda}{\in}{\Lambda},\;x{\in}(a,b)$$, where ${\Lambda}$ is an index set consisting of the non-negative real numbers, and $n{\geq}1$ is a finite natural number, at ${\mu}$-generalized Lebesgue points of integrable function $f{\in}L_1(a,b)$. Here, $f^m$ denotes m-th power of the function f and (a, b) stands for arbitrary bounded interval in ${\mathbb{R}}$ or ${\mathbb{R}}$ itself. We also handled the indicated problem under the assumption $f{\in}L_1({\mathbb{R}})$.

• The KIPS Transactions:PartA
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• v.18A no.6
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• pp.225-232
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• 2011

Restricted Hypercube-Like (RHL) graphs are a graph class that widely includes useful interconnection networks such as crossed cube, Mobius cube, Mcube, twisted cube, locally twisted cube, multiply twisted cube, and generalized twisted cube. In this paper, we show that for an m-dimensional RHL graph G, $m{\geq}4$, with an arbitrary faulty edge set $F{\subset}E(G)$, ${\mid}F{\mid}{\leq}m-2$, graph $G{\setminus}F$ has a hamiltonian path between any distinct two nodes s and t if dist(s, V(F))${\neq}1$ or dist(t, V(F))${\neq}1$. Graph $G{\setminus}F$ is the graph G whose faulty edges are removed. Set V(F) is the end vertex set of the edges in F and dist(v, V(F)) is the minimum distance between vertex v and the vertices in V(F).

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1139-1161
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• 2012

Let $p$ be an odd prime number and let F be a finite field with $p^m$ elements. We study representations and strict representations of polynomials $M{\in}F$[T] by sums of ($p^r$ + 1)-th powers. A representation $$M=M_1^k+{\cdots}+M_s^k$$ of $M{\in}F$[T] as a sum of $k$-th powers of polynomials is strict if $k$ deg $M_i<k$ + degM.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• Journal of the Korean Magnetics Society
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• v.6 no.4
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• pp.264-271
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• 1996

A magnetically shielded room has been constructed for biomagnetic applications. The room has internal dimensions of $2\;m(length){\times}2\;m(width){\times}2.5\;m(height)$ and it consists of high permeability Mumetal and high conductivity alummum, utilizing ferromagnetic shielding and eddy current shielding. The de shielding factor around the center of the room is above 60 dB, and the ac shielding factors at 1 and 10 Hz are larger than 60 and 80 dB, respectively. The internal magnetic field noise at 1 Hz is $500\;fT/{\sqrt}Hz$ and at 10 Hz is $100\;fT/{\sqrt}Hz$, and the field gradient noise at 1 Hz is below $7\;fT/cm{\sqrt}Hz$. Successful measurements of cardiomagnetic fields usmg SQUID magnetometer and neuromagnetic fields using SQUID gradiometer have been done.